The nearest thing to an 'official' name the American Flag flag, and is one of the names used in US Government text when refering to the flag, a name much in the tradition of banners like the Union Jack, Red Ensign and other.
The name 'Old Glory' is in honour of Salem, Mass. shipmaster Captain Stephen Driver, and was coined by him in 1831. On a later voyage he was given an a US flag and as he unfurled it in the breeze, he exclaimed 'I shall name her Old Glory', and thus it stuck. When Driver left the life of the sea and settled in Nashville in 1937 he naturally brought his treasured banner with him and flew it on a rope from his house to a tree across the street.
When Tennessee seceded from the Union, Rebels became bent on destroying Drivers 'Old Glory' but were never able to find it even after repeated (unauthorized] searches of Drivers home.
in February of 1862, Nashville was recaptured and an American Flag was raised over the capital. It was said by many to be too small to be worthy and asked Driver if his Grand 'Old Glory' still was around, or if it had been destroyed as so many feared. Driver returned home, ripped the quilting off his mattress and produced none other than Old Glory herself and was granted the opportunity to have it flown over the capitol.
He eventually passed his flag on to his daughter and remained in his family until 1922 when it was given to the Smithsonian Institution.